Hello
To apply and get ADMINISTRATION Granted to you, you had to be NEXT OF KIN to the Deceased (in a set order), or the Legal Representative acting for the Next of Kin (and both names appear in the Calendar).
And also the deceased person left no Will, meaning they died Intestate.
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A thorough knowledge of your family tree, should hopefully clear up your query.
Applying for post 1858 Administrations, often don't give much more away, unless it says Administration with Will.
But as Family Historians, we should always endeavour to obtain the original paperwork, to check for any comment.
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I applied for two delayed 1880 England Administrations. I was already aware that three Sisters (all Spinsters) had died from 1853 to 1855.
The Mother of the 3 Daughters (dying 1853 to 1855) died in 1879 and had obviously kept items belonging to two of her late Daughters (who had no Children). When their Mother died 1879, the Spinsters Brother claimed Administration in 1880.
There was a Legal 'pecking order', as it were.
Administrators, had to follow the Law and not their emotions.
My comments are not Legal Advice -----------
This is quite interesting
https://www.gov.uk/inherits-someone-dies-without-willMark